Method of removing noise and interference from signal

ABSTRACT

A method of removing noise and interference from a signal by receiving the signal, calculating a joint time-frequency domain of the signal, estimating instantaneous frequencies of the joint time-frequency domain, modifying each estimated instantaneous frequency, if necessary, to correspond to a frequency of the joint time-frequency domain to which it most closely compares, redistributing the elements within the joint time-frequency domain according to the estimated instantaneous frequencies as modified, computing a magnitude for each element in the joint time-frequency domain as redistributed, plotting the results as the time-frequency representation of the signal, identifying in the plot any noise and interference components in the received signal, eliminating from the redistributed joint time-frequency domain elements that correspond to noise and interference, and recovering a signal devoid of noise and interference from the modified redistributed joint time-frequency domain.

FIELD OF INVENTION

The present invention relates, in general, to speech signal processingand, in particular, to noise and interference reduction.

BACKGROUND OF THE INVENTION

A frequently recurring problem in communications is the need to removenoise and interference from a signal. There have been many approachessuggested to address this problem. For stationary narrowbandinterference, a simple notch filter may be effective. Adaptive notchfilters have been suggested to remove narrowband non-stationaryinterference. For removal of broadband noise from speech, Wiener filtertechniques such as spectral subtraction are frequently used.

An adaptive filter can be used to remove a single non-stationarynarrowband interfering signal from a broadband, or speech, signal. Inthis process, the frequency of the interfering signal is estimated ateach time, and a single estimate of the interfering signal bandwidth isestimated. The received signal is frequency shifted at each time suchthat the frequency of the interfering signal is constant in the shiftedrepresentation. A fixed notch filter is applied to remove theinterfering signal, and the filtered signal is frequency shifted to itsoriginal frequency. This process can remove a single interferingnarrowband signal and it can, in principle, be iterated to removeseveral interfering signals. However, the primary problem with using anadaptive filter is that the instantaneous frequency of the interferencemust be accurately estimated at each time. Such estimation is difficult.Furthermore, an adaptive filter cannot be used to remove noise.

In Wiener filtering, or spectral subtraction, components which aredominated by noise are removed from the spectrogram, and the noise-free,or clean, signal is estimated by a pseudo inversion process. Spectralsubtraction is the most common enhancement method used in speechprocessing. In this method, a short time Fourier transform (STFT) iscomputed. The STFT is a time-frequency representation. STFT componentsidentified as dominated by noise are reduced in magnitude, and a signalwhose STFT approximates the modified STFT is computed. The clean signalestimated this way is only an approximate solution because the modifiedSTFT cannot be inverted. In the pseudo inversion process, some ad hoccriterion must be used. Furthermore, spectral subtraction cannot beeasily used to remove narrowband interference.

For stationary narrowband interference, a clean signal can be estimatedby using a notch filter which is tuned to the interference frequency andbandwidth. A notch filter cannot remove noise or interference whosefrequencies change with time.

None of the prior art methods adequately identify and separate signaland non-stationary interference components.

U.S. Pat. No. 6,175,602, entitled “SIGNAL NOISE REDUCTION BY SPECTRALSUBTRACTION USING LINEAR CONVOLUTION AND CASUAL FILTERING,” discloses amethod of reducing noise in a signal by spectral subtraction. Thepresent invention does not use spectral subtraction as does U.S. Pat.No. 6,175,602. U.S. Pat. No. 6,175,602 is hereby incorporated byreference into the specification of the present invention.

U.S. Pat. No. 6,266,633, entitled “NOISE SUPPRESSION AND CHANNELEQUALIZATION PREPROCESSOR FOR SPEECH AND SPEAKER RECOGNIZERS: METHOD ANDAPPARATUS,” discloses a device for and method of noise suppression thatuses blind deconvolution. The present invention does not use blinddeconvolution as does U.S. Pat. No. 6,266,633. U.S. Pat. No. 6,266,633is hereby incorporated by reference into the specification of thepresent invention.

U.S. Pat. No. 6,795,559, entitled “IMPULSE NOISE REDUCER DETECTINGIMPULSE NOISE FROM AN AUDIO SIGNAL,” discloses a method of reducingnoise by detecting and smoothing the high frequency amplitude of asignal, attenuating the non-smoothed amplitude of the signal, comparingthe attenuated amplitude to a threshold, and identifying and removingthe noise. The present invention does not smooth the high frequencyamplitude of a signal as does U.S. Pat. No. 6,795,559. U.S. Pat. No.6,795,559 is hereby incorporated by reference into the specification ofthe present invention.

U.S. Pat. No. 6,801,889, entitled “TIME-DOMAIN NOISE SUPPRESSION,”discloses a method of reducing noise by performing a Fourier Transformon the signal to generate a frequency spectrum, performing an InverseFourier Transform to simulate a noise signal, and subtracting thesimulated noise signal from the time-domain signal. The presentinvention does not simulate noise using an Inverse Fourier Transform asdoes. U.S. Pat. No. 6,801,889. U.S. Pat. No. 6,801,889 is herebyincorporated by reference into the specification of the presentinvention.

U.S. Pat. No. 6,826,392, entitled “MULTIPATH NOISE REDUCTION METHOD,MULTIPATH NOISE REDUCER, AND FM RECEIVER,” discloses a method ofreducing noise by frequency modulating the signal, extracting ahigh-frequency

signal from the modulated signal, generating a noise reductioncoefficient from the extracted high-frequency signal, separating thesignal into high-frequency and low frequency components, multiplying thehigh-frequency component by the noise reduction coefficient, and addingthe product to the low-frequency component. The present invention doesnot generate a noise reduction coefficient as does U.S. Pat. No.6,826,392. U.S. Pat. No. 6,826,392 is hereby incorporated by referenceinto the specification of the present invention.

U.S. Pat. Appl. No. 20020173276 A1, entitled “METHOD FOR SUPPRESSINGSPURIOUS NOISE IN A SIGNAL HELD,” discloses a method of reducing noiseby determining a distribution function of the signal, comparing thedistribution to a reference distribution, modifying the components inthe signal that differ from the reference distribution, and notmodifying the components in the signal that are the same as those in thereference distribution. The present invention does not use a referencedistribution as does U.S. Pat. Appl. No. 20020173276 A1. U.S. Pat. Appl.No. 20020173276 A1 is hereby incorporated by reference into thespecification of the present invention.

SUMMARY OF THE INVENTION

It is an object of the present invention to remove noise andinterference from a speech signal.

It is another object of the present invention to remove noise andinterference from a speech signal by concentrating a short time Fouriertransform (STFT) and estimating a noise-free and interference-freesignal by integration.

The present invention is a method of removing noise and interferencefrom a speech signal by concentrating a STFT and estimating a noise-freeand interference-free signal by integration.

The first step of the method is receiving the signal.

The second step of the method is converting the received signal to thejoint time-frequency domain.

The third step of the method is estimating an instantaneous frequency(IF) for each element in the joint time-frequency domain calculated inthe second step.

The fourth step of the method is modifying each result of the thirdstep, if necessary, where each IF element is replaced, if necessary,with the discrete frequency of the joint time-frequency domain createdin the second step to which it most closely compares in value.

The fifth step of the method is redistributing the elements within thejoint time-frequency domain created in the second step according to theIF elements as modified by the fourth step.

The sixth step of the method is computing, for each time, the magnitudesof each element of the joint time-frequency domain as redistributed inthe fifth step.

The seventh step of the method is plotting the results of the sixth stepin a graph as the time-frequency representation of the received signal.

The eighth step of the method is identifying in the plot of the seventhstep any noise and interference components in the received signal.

The ninth step of the method is eliminating from the redistributed jointtime-frequency domain those elements that correspond to noise andinterference identified in the eighth step.

The tenth, and last, step of the method is recovering a signal devoid ofnoise and interference from the redistributed joint time-frequencydomain as modified in the ninth step.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart of the steps of the present invention.

DETAILED DESCRIPTION

The present invention is a method of removing noise and interferencefrom a signal.

FIG. 1 is a flowchart of the method of the present invention.

The first step 1 of the method is receiving the signal. The signal maybe in the time or frequency domain. In the preferred embodiment, thereceived signal is in the time domain.

The second step 2 of the method is converting the received signal to thejoint time-frequency domain. In the preferred embodiment, the secondstep 2 is accomplished by calculating a short-time Fourier transform(STFT) on the received speech signal. An STFT is a known method offorming a matrix of complex values that represent the signal, where thecolumns (or rows) of the matrix are discrete time and the rows (orcolumns) of the matrix are discrete frequency. The elements of thematrix may be thought of as representing a complex-valued surface. AnSTFT is computed by selecting a window size, selecting a window-sizedportion of the received signal, and performing a Fourier Transform onthe selected portion of the signal. Another window is selected and thesteps are repeated. In the preferred embodiment, a subsequently selectedwindow overlaps the previously selected window (e.g., all but one samplein the new window is the same as the previous window). Each element ofthe resulting STFT matrix is of the following form:z=x+iy,Represented in time and frequency, each element of the matrix is of thefollowing form:z(t,ω)=x(t,ω)+iy(t,ω),The representation in time and phase may be represented in polar form asfollows:z(t,ω)=√{square root over (x ²(t,ω)+y ³(t,ω))}{square root over (x²(t,ω)+y ³(t,ω))}×e ^(iφ(t,ω)),where φ(t,ω) is the argument (arg) of the element, and where

$\arg = {{\tan^{- 1}\left( \frac{y\left( {t,\omega} \right)}{x\left( {t,\omega} \right)} \right)}.}$

The third step 3 of the method is estimating an instantaneous frequency(IF) for each element in the STFT matrix calculated in the second step2. The result is an IF matrix, where the rows and columns are the samediscrete times and frequencies as those of the STFT matrix, and whereeach IF is located in the IF matrix at the same time and frequency asthat of its corresponding STFT element. In the preferred embodiment, theIFs are estimated for the elements of the STFT matrix by finding theargument for each element in the STFT matrix, forming an argumentmatrix, and calculating the derivative of the argument matrix withrespect to time. The result is an IF matrix, where an element in the IFmatrix is the IF of the corresponding element in the STFT matrix.

The fourth step 4 of the method is modifying each result of the thirdstep 3, if necessary, where each element in the IF matrix is replaced,if necessary, with the discrete frequency of the STFT matrix created inthe second step 2 to which it most closely compares in value. Forexample, if the discrete frequencies in the STFT matrix are 1 Hz, 2 HZ,. . . , then an IF matrix element of 1.4 Hz would be changed to 1 Hz,while an IF matrix element of 1.6 would be changed to 2 Hz, and an IFmatrix element of 2 Hz would not be changed.

The fifth step 5 of the method is redistributing the elements within theSTFT matrix created in the second step 2 according to the IF matrix asmodified by the fourth step 4 by identifying an STFT matrix element'scorresponding element in the IF matrix, determining the value of thecorresponding IF matrix element, and moving the STFT matrix elementwithin its column to the row that corresponds to the value of thecorresponding IF matrix element. If two elements of the STFT matrix mapto the same row then sum those STFT elements and place the result at therow. In the following example, an STFT matrix of complex-valuedelements, represented by letters of the alphabet for simplicity, will beremapped according to a modified IF matrix. The columns of the STFTmatrix are in time (i.e., 1-4 msecs.), and its rows are in frequency(i.e., 1-4 Hz.). Each element in the modified IF matrix corresponds to acolumn value in the STFT matrix.

STFT Matrix 1 msec. 2 msec. 3 msec. 4 msec. 1 Hz. A E I M 2 Hz. B F J N3 Hz. C G K O 4 Hz. D H L P

Modified IF Matrix 1 msec. 2 msec. 3 msec. 4 msec. 1 Hz. 2 3 2 3 2 Hz. 43 2 3 3 Hz. 2 1 4 1 4 Hz. 4 1 4 1

Remapped STFT Matrix 1 msec. 2 msec. 3 msec. 4 msec. 1 Hz. G + H O + P 2Hz. A + C I + J 3 Hz. E + F M + N 4 Hz. B + D K + L

The result of the fifth step 5 is a novel time-frequency representation.When applied to a multi-component signal which has linearly independentcomponents and which are separable, the method produces a time-frequencyrepresentation in which the value of each signal component isdistributed, or concentrated, along the component's instantaneousfrequency curve in the time-frequency plane. The concentrated STFT is alinear representation, free of cross-terms, which plagued the prior artmethods, and having the property that signal and interference componentsare easily recognized because their distributions are more concentratedin time and frequency. A plot of the remapped matrix is necessary to seethat the elements have been so remapped. The following steps result insuch a plot.

The sixth step 6 of the method is computing, for each time, themagnitudes of each element in the redistributed STFT matrix of step (e).The result is a matrix of magnitudes, where the elements of themagnitude matrix map to the element in the redistributed matrix to whichthe magnitudes correspond.

The seventh step 7 of the method is plotting the results of the sixthstep 6 in a graph as the time-frequency representation of the receivedsignal, where one axis is time, and the other axis is frequency. Theresult is a focused representation of each signal component of thereceived signal, where the phase information of the received signal isretained. Prior art methods do not retain such phase information. Thecomponents of the signal may include the intended signal, random noise,and interference (i.e., one or more unintended periodic signal).

The eighth step 8 of the method is identifying in the plot of theseventh step 7 any noise and interference components in the receivedsignal. Noise and interference is identified by comparing the magnitudesof the plot of the seventh step 7 to a user-definable threshold.Magnitudes in the plot of the seventh step 7 that are below thethreshold are considered random noise, while magnitudes above thethreshold are considered intended signal components and interferencecomponents. Interference components are then identified by visualinspection. Any periodic signal in the plot that appears to not belongis identified as interference.

The ninth step 9 of the method is eliminating from the redistributedjoint time-frequency domain those elements that correspond to noise andinterference identified in the eighth step 8. Elements are identified inthe magnitude matrix computed in the sixth step 6 that are associatedwith noise and interference. Then, the elements in the redistributedjoint time-frequency domain that correspond to the identified magnitudesare eliminated (e.g., zeroed out).

The tenth, and last, step 10 of the method is recovering a signal devoidof noise and interference from the redistributed joint time-frequencydomain as modified in the ninth step 9. The tenth step 10 isaccomplished by summing each column or row, whichever representsdiscrete time, in the redistributed joint time-frequency domain asmodified by the ninth step 9 and listing the results, in sequence, asthe received signal devoid of noise and interference. In the exampleabove, the columns of the remapped STFT matrix are indexed in time,while the rows are indexed in frequency. In the example, the columnswould be summed.

1. A method of removing noise and interference from a signal, comprisingthe steps of: a) receiving the signal; b) calculating a jointtime-frequency domain of the received signal; c) estimatinginstantaneous frequencies of the joint time-frequency domain; d)modifying each estimated instantaneous frequency, if necessary, tocorrespond to a frequency of the joint time-frequency domain to which itmost closely compares; e) redistributing the elements within the jointtime-frequency domain according to the estimated instantaneousfrequencies as modified; and f) computing a magnitude for each elementin the joint time-frequency domain as redistributed; g) plotting theresults of the step (f) as the time-frequency representation of thereceived signal; h) identifying in the plot of step (g) any noise andinterference components in the received signal; i) eliminating from theredistributed joint time-frequency domain elements that correspond tothe noise and interference identified in step (h); and j) recovering asignal devoid of the noise and interference from the redistributed jointtime-frequency domain as modified in step (i).
 2. The method of claim 1,wherein the step of receiving a signal, is comprised of receiving asignal, where the signal includes an intended signal, at least on signalcomponent selected from the group of signal components consisting of aninterfering signal, and the noise.
 3. The method of claim 1, wherein thestep of calculating a joint time-frequency domain of the received signalis comprised of the step of calculating a short-time Fourier Transformof the signal received in step (a), where the result is in matrix form,where the rows and columns represent discrete frequencies and times in auser-definable manner.
 4. The method of claim 3, wherein the step ofcalculating a short-time Fourier Transform is comprised of the step ofselecting a window size, selecting a window-sized portion of thereceived signal, performing a Fourier Transform on the selected portionof the received signal, selecting a next window, where the next windowoverlaps a user-definable amount with the window selected just prior tothe next window, selecting a next portion of the received window inaccordance with the next window selected, performing a Fourier Transformon the next portion of the received signal, and repeating these stepsuntil the entire received signal has been processed.
 5. The method ofclaim 3, wherein the step of estimating instantaneous frequencies of thejoint time-frequency domain is comprised of the step of estimatinginstantaneous frequencies of the short-time Fourier Transform calculatedin step (b).
 6. The method of claim 5, wherein the step of estimatinginstantaneous frequencies of the short-time Fourier Transform iscomprised of the steps of: (a) determining arguments for each element inthe short-time Fourier Transform matrix; (b) forming an argument matrixfrom the results of step (a), where each element in the argument matrixcorresponds to the element in the short-time Fourier Transform matrixfrom which the argument was determined; (c) calculating a derivative ofthe argument matrix; and (d) forming an instantaneous frequency matrixfrom the results of step (c), where each element in the instantaneousfrequency matrix corresponds to the element in the argument matrix fromwhich the instantaneous frequency matrix element was derived.
 7. Themethod of claim 3, wherein the step of modifying each estimatedinstantaneous frequency, if necessary, to correspond to a frequency ofthe joint time-frequency domain calculated in step (b) to which it mostclosely compares is comprised of the step of modifying eachinstantaneous frequency, if necessary, to the closest discrete frequencyof the short-time Fourier Transform of step (b).
 8. The method of claim3, wherein the step of redistributing the elements within the jointtime-frequency domain according to the instantaneous frequencies asmodified in step (d) is comprised of the step of redistributing theelements within the short-time Fourier Transform according to theinstantaneous frequencies.
 9. The method of claim 8, wherein the step ofredistributing the elements within the short-time Fourier Transformaccording to the instantaneous frequencies is comprised of the steps of:(a) identifying, for each element in the short-time Fourier Transform,the instantaneous frequency that corresponds position-wise to theelement in the short-time Fourier Transform; (b) identifying the valueof the identified instantaneous frequency; and (c) moving thecorresponding element in the short-time Fourier Transform to thelocation within its matrix column that corresponds to the identifiedvalue of the corresponding instantaneous frequency, summing all of theshort-time Fourier Transform elements that map to the same location. 10.The method of claim 1, wherein the step of identifying in the plot ofstep (g) any noise and interference components in the received signal iscomprised of the steps of: (a) comparing the magnitudes of the plot ofstep (g) to a user-definable threshold; (b) identify magnitudes belowthe user-definable threshold as noise; (c) identify magnitudes above theuser-definable threshold intended signal components and interferencecomponents; and (d) determining which of the results of step (c) do notmeet a user-definable criteria for being interference, identifying suchresults as interference and the remaining results as intended signalcomponents.
 11. The method of claim 1, wherein the step of eliminatingfrom the redistributed joint time-frequency domain elements thatcorrespond to noise and interference identified in the step (h) iscomprised of the steps of: (a) identifying elements in the magnitudematrix computed in step (f) that are associated with the noise andinterference; and (b) eliminating the elements in the redistributedjoint time-frequency domain that correspond to the identifiedmagnitudes.
 12. The method of claim 1, wherein the step of recovering asignal devoid of noise and interference from the redistributed jointtime-frequency domain as modified in step (i) is comprised of the stepsof: (a) summing the matrix axis that represents discrete time in theredistributed joint time-frequency domain as modified by step (i); and(b) listing the results of step (b), in sequence, as the received signaldevoid of the noise and interference.